openSSH for Windows: Domain Admin access with SSH Key

OpenSSH for Windows version: 8.6
Server OperatingSystem: W2k16, W2k19, W2k22
Client OperatingSystem: W10Pro

What is failing
We've configured openSSH for Windows and accessing it with public/private keys. To allow domain admins to join via SSH, we use the following config line:
AllowGroups "DOMAIN\Domain Admins"

It's possible to login and I'm able to invoke administrative commands but as soon as I'm trying to connect to the active directory domain or use Exchange Powershell cmdlets, I get the following error message:

PS C:\Users\Administrator.DOMAIN> Get-ADUser -Filter *
Get-ADUser : Unable to contact the server. This may be because this server does not exist, it is currently down, or it does not have the Active Directory Web Services
running.
At line:1 char:1
+ Get-ADUser -Filter *
+ ~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : ResourceUnavailable: (:) [Get-ADUser], ADServerDownException
    + FullyQualifiedErrorId : ActiveDirectoryServer:0,Microsoft.ActiveDirectory.Management.Commands.GetADUser

PS C:\Users\Administrator.DOMAIN> Get-ExchangeServer
Active Directory operation failed on . The supplied credential for 'DOMAIN\Administrator' is invalid.
At line:1 char:1
+ Get-ExchangeServer
+ ~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : NotSpecified: (:) [], ADInvalidCredentialException
    + FullyQualifiedErrorId : [Server=EX0401,RequestId=a1317adf-797b-47b8-9334-392b2ae48768,TimeStamp=04.01.2022 14:29:41] [FailureCategory=Cmdlet-ADInvalidCredentialExc
   eption] 3C6659B2

If I login with domain username/password combination, it's working fine. So it seems like that it's not possible to run domain cmdlets if I'm using SSH key for authentication. Could that be true? Have I missed something?

Start with the reported OpenSSH 8.6 setup on Windows Server 2016/2019/2022 and the AllowGroups "DOMAIN\Domain Admins" configuration. Reproduce the difference between SSH-key and password authentication by running Get-ADUser -Filter * and Get-ExchangeServer in PowerShell. Done means establishing whether this is an OpenSSH limitation or configuration issue and documenting a confirmed resolution or reproduction.